This chocolate babka is rich, decadent and can be made at home in only a few hours.
In a 4-cup measuring cup or medium bowl, stir together the milk and yeast and let sit for 5 minutes. Then, whisk in the sugar, egg, and egg yolk.
In the bowl of an electric mixer fitted with the dough hook, add the flour and salt. Mix on low speed to combine, about 1 minute. Add the yeast mixture and mix until most of the flour has been incorporated, about 1 minute.
Add the butter a few chunks at a time and knead until the dough forms a soft, smooth dough that is just slightly sticky when squeezed together, about 5 to 10 minutes. Turn the dough out onto a lightly floured surface and knead just a few times until the dough is smooth, then place in a greased bowl, turning to coat the dough. Cover with plastic wrap and place in a warm, draft-free spot to rise until doubled in size, about 1 hour.
In a large bowl, stir together the chopped chocolate, sugar, and cinnamon. Add the butter and, using a pastry blender or a fork, cut the butter into the mixture until completely combined.
In a small bowl, whisk together the egg and heavy cream.
Grease two 9x5-inch loaf pans with butter, then line with parchment paper; set aside. Gently punch down the dough, then turn out to a clean work surface and allow to rest for 5 minutes.
Divide the dough in half and keep the half you are not working with covered with plastic wrap.
On a well-floured surface, roll the dough into a 16-inch square. Crumble half of the filling over the surface of the dough, reserving 2 tablespoons of the filling, and leaving a ½-inch border around the edges of the dough.
Brush the egg wash around the border of the dough. Starting at one side, roll the dough up tightly into a log, pinching the ends together to seal. Holding one end of the dough in each hand, twist the dough lengthwise five or six times.
Brush the top of the log with the egg wash, then carefully sprinkle the remaining 2 tablespoons of filling over the top of the log, pressing it into the egg wash. If any falls off the sides, pick it up and press it into the top.
Fold the dough in half into a horseshoe shape, then cross the right half over the left half. Pinch the ends together to seal and form a figure eight. Holding one end of the dough in each hand, twist the dough two more times, then nestle it into the prepared loaf pan.
Repeat steps #9 through #12 with the second half of dough.
Preheat oven to 350 degrees F with rack in lower third of oven.
In a medium bowl, whisk together the powdered sugar and flour. Using a pastry blender or fork, cut in the butter until the mixture resembles coarse crumbs with larger chunks throughout.
Brush the top of each loaf with the egg wash and sprinkle each loaf evenly with half of the streusel topping. Cover the loaves loosely with plastic wrap and place in a warm, draft-free spot until the dough has expanded and puffed a bit, about 30 minutes.
Bake the loaves, rotating halfway through, until a light golden brown, about 55 minutes. Reduce the oven temperature to 325 degrees F and continue baking until deep golden brown and a digital instant-read thermometer inserted into the center of the loaves registers 190 degrees F, about 15 to 30 more minutes. Transfer the pans to wire racks to cool completely. The loaves should be wrapped tightly in plastic wrap and can be stored at room temperature for up to 4 days.